River mouths building into standing bodies of water have strikingly varied growth habits. This presents a compelling pattern formation problem that is also of great practical relevance for subsurface prediction and managing coastal wetlands. Here we present a generalized 2.5-dimensional potential vorticity (PV) theory that explains sedimentation patterns of a sediment-laden stationary jet by coupling an understanding of vorticity with suspended sediment concentration fields. We explore the physical meaning of this new sediment-PV definition, and its impact on outflow depositional patterns, by analyzing data from a shallow wall-bounded plane jet experiment and by discussing new theoretical insights. A key result is that lateral advection and diffusion of suspended sediment are directly proportional to jet vorticity, a feature that reveals the mechanistic process that forms elongated channels by focused levee deposition. The new PV theory constitutes a more generalized mathematical framework that expands the Rouse theory for the equilibrium of suspended sediment.